arXiv subjects

Mihai Mihăilescu

Publications and source records attributed to Mihai Mihăilescu.

4 recordsLinked to original sources

arXiv2016

On a non-homogeneous eigenvalue problem involving a potential: an Orlicz-Sobolev space setting

In this paper we study a non-homogeneous eigenvalue problem involving variable growth conditions and a potential $V$. The problem is analyzed in the context of Orlicz-Sobolev spaces. Connected with this problem we also study the optimization problem for the particular eigenvalue given by the infimum of the Rayleigh quotient associated to the problem with respect to the potential $V$ when $V$ lies in a bounded, closed and convex subset of a certain variable exponent Lebesgue space.

math.AP↗

arXiv2016

An eigenvalue problem involving a degenerate and singular elliptic operator

We study an eigenvalue problem involving a degenerate and singular elliptic operator on the whole space $\mathbb{R}^N$. We prove the existence of an unbounded and increasing sequence of eigenvalues. Our study generalizes to the case of degenerate and singular operators a result of A. Szulkin and M. Willem.

math.AP↗

arXiv2016

Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz-Sobolev spaces

We study a non-homogeneous boundary value problem in a smooth bounded domain in $\mathbb{R}^N$. We prove the existence of at least two nonnegative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma.

math.AP↗

arXiv2016

On a PDE involving the ${\cal A}_{p(\cdot)}$-Laplace operator

This paper establishes existence of solutions for a partial differential equation in which a differential operator involving variable exponent growth conditions is present. This operator represents a generalization of the $p(\cdot)$-Laplace operator, i.e. $Δ_{p(\cdot)}u={\rm div}(|\nabla u|^{p(\cdot)-2}\nabla u)$, where $p(\cdot)$ is a continuous function. The proof of the main result is based on Schauder's fixed point theorem combined with adequate variational arguments. The function space setting used here makes appeal to the variable exponent Lebesgue and Sobolev spaces.

math.AP↗